Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 4x - 1$ and $ KL = 5x - 3$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {4x - 1} = {5x - 3}$ Solve for $x$ $ -x = -2$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 4({2}) - 1$ $ KL = 5({2}) - 3$ $ JK = 8 - 1$ $ KL = 10 - 3$ $ JK = 7$ $ KL = 7$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {7} + {7}$ $ JL = 14$